When two bodies are attracted to each other their motion leaves their center of mass unchanged. They effectively revolve around
their center of mass. Let r1 and r2 denote the vectors of
the positions of two bodies with respect to their center of mass.

The operative equation for examining two-body systems is:

r2 = -(m1/m2)r1

Illustrations of the Two-Body Systems

If the Earth were the only satellite of the Sun and the Earth were moving in an elliptical orbit about the center of mass of the
Sun-Earth system then the Sun would also be moving in an elliptical orbit about that same center of mass. The scales of the orbits
would be in proportion to the ratio of the masses. The Sun is about 333 thousand times as massive as the Earth. Thus if the
average radius of the Earth's orbit is 93 million miles (150 million km) then the radius of the Sun's counter orbit is about 280 miles (450 km).
The center of mass of the Sun-Earth system is well within the body of the Sun.

When the orbits are elliptical the orbit is with respect to one of the foci of the ellipse. The counter orbit of the other body
is with respect ot the opposite foci for its ellipse. This has to be the case so both bodies reach their apogees (maximum distances) and
perigees (minimum distances) at the same time.

For the Sun-Jupiter system the magnitude of the Sun's counter orbit is not so insignificant. The mass of the Sun is only about
1050 times as large as that of Jupiter. The radius of Jupiter's orbit around the center of mass of the two bodies is about
484 million miles so the radius of the Sun's counter orbit around their center of mass would be about 462 thousand miles. This is
about 28 thousand miles above the surface of the Sun.

For the Earth-Moon system the statistics are that the ratio of the mass of the moon to that of the Earth is 0.0123 and therefore
since the radius of the Moon's orbit is about 240 thousand miles (384 thousand km) the radius of the orbit that the Earth would move in
with respect to the Earth-Moon center of mass if
there were no other bodies in the solar system is about three thousand miles (4700 km). Since the radius of the Earth's radius is approximately
four thousand miles the center of mass of the system is about a thousand miles below the surface of the Earth. Because the Earth is
rotating that center of mass is not at a fixed location with respect to the Earth's features. In other words, the Earth rotates through
that center of mass so it is under different points of the Earth's surface at different times of the day.

The figures for the orbits and counter orbits for other two-body systems in the solar system are given below:

Distances of the Sun from the Center of Mass for
It and Various
Planets

Planet

Orbit Radius

Mass Ratio

Radius of Sun'sCounter Orbit

Earth

93 million miles

333,000

280 miles

Jupiter

484 million miles

1050

462,000 miles

Saturn

839 million miles

3445

244,000 miles

Uranus

1.8 billion miles

22,900

78,000 miles

Neptune

2.8 billion miles

19,400

144,000

Venus

67.6 million miles

408,000

166 miles

Mercury

36 million miles

6 million

6 miles

The center of mass of the entire solar system does not not deviate from the center of mass of the Sun as much as it does for the
the two-body combinations shown above. This is because planets on the opposite sides of the Sun cancel out their individual effects.